increasing amount of side faces on object made from cylinder
Mesh Objects in Blender don't have an Edit History that would allow you to edit a parameter somewhere at the start of the Object's life and have that propagate through all other operations to the present. You can't in your example change the tube's vertex count after you've made edits to it.

But it is possible to reconstruct the object quickly with the desired vertex counts. For instance use the Screw Modifier to Lathe the profile around an axis. The Object's center can be used as the rotation coordinate or an Empty.